727 Torqueflight will not go into reverse

Thanks everyone for the info. I know nothing about automatic transmissions and really have no way to get the pan off and have a look. I sold the car lift we used during the building of the car. I am trailering the car to a local shop tomorrow (Tuesday, Feb. 24th) that seems very knowable about these transmissions. I can't wait for them to tell me what's wrong. They will also be fixing the reverse lights - they stay on even when in drive and also recalabrating the speedo to compensate for the larger tires my buddy put on the car.

I'll report back soon.